Mathematical theology of experience

Mathematical Theology: Future Science of Confidence in Belief (Part #7)

As noted above, Davis and Hersh (1981) have given a focus to "mathematical experience", as a prelude to an exploration of mathematical theology by Davis (2004), and futher articulation of the experience by Hersh (2006, 2010). The remarks of Gregory Chaitin are of value (Metamaths: the quest for omega, 2005):

In my opinion, the view that math provides absolute certainty and is static and perfect while physics is tentative and constantly evolving is a false dichotomy. Math is actually not that different from physics. Both are attempts by the human mind to organize, to make sense of, human experience; in the case of physics, experience in the laboratory, in the physical world; and in the case of math, experience in the computer, in the mental mindscape of pure mathematics. (pp. 7-8)

Might analogous distinctions be appropriately made between mathematics and theology? Chaitin continues:

And mathematics is far from static and perfect; it is constantly evolving, constantly changing, constantly morphing itself into new forms. New concepts are constantly transforming math and creating new fields, new viewpoints, new emphasis, and new questions to answer. And mathematicians do in fact utilize unproved new principles suggested by computational experience, just as a physicist would (p. 8).

Is this not the appropriate manner in which to frame the ecology of beliefs on which a reframed theology might focus? However, in terms of the case for self-reference, to what extent does any theory embody the probability of the emergence of a new theory, rather than implying it is a form of "theory of everything" for eternity? Chaitin continues:

And in discovering and creating new mathematics, mathematicians do base themselves on intuition and inspiration, on unconscious motivations and impulses, and on their aesthetic sense, just like any creative artist would. (p. 8)

This could readily describe the experience of anyone exploring the possibility and credibility of systems of belief. Again he continues:

And mathematicians do not lead logical mechanical "rational" lives. Like any creative artist, they are passionate emotional people who deeply care about their art, they are unconventional eccentrics motivated by mysterious forces, not by money nor by concern for the "practical applications" of their work. (p. 8)

Here he precludes the possibility of multiple styles in the approach to such matters, exemplified by the archetypal contrasts explored by Hermann Hesse (Narcissus and Goldmund, 1930) -- and more systematically by W. T. Jones (The Romantic Syndrome; toward a new methodology in cultural anthropology and the history of ideas, 1961), as summarized separately (Axes of Bias in Inter-Cultural Dialogue, 1993).

Integral awareness: Various authors have endeavoured to articulate, directly or by implication, how spiritual insight and intuition are informed and enabled by mathematics. Citing Georg Cantor's work on infinity, the focus of Sarah Voss on "mathaphors" is helpful in this respect (Mathematics and Theology: a stroll through the Garden of Mathaphors, Theology and Science, 2006). How do complex geometrical symbols, like yantras, assist in this process during the course of meditation?

Jennifer Gidley provides a very comprehensive integral hermeneutic analysis of the evolutionary writings of Rudolf Steiner and Ken Wilber in the light of Jean Gebser's structures of consciousness (The Evolution of Consciousness as a Planetary Imperative: an integration of integral views, Integral Review, 2007). The explicitly "pluralistic narrative tapestry" seemingly dissociates, to a significant degree, the current role of mathematics in favour of another mode of discourse more characteristic of theology and of the integrative writers she so usefully summarizes.

Gidley notes the work of L. Kuhn and R. Woog (From complexity concepts to creative applications, World Futures, 2007) in undertaking pioneering postformal research, by taking several key concepts from complexity science -- originally formulated as mathematical concepts -- and reshaping them in prose, as a basis for social inquiry, e.g., fractal dimensions become fractal narratives; mathematical phase space becomes phrase space as a literary device related to construct awareness in narrative and discourse.

Gidley cites Kant (1781/1929) to the effect that: Mathematics gives us a shining example of how far, independently of experience, we can progress in a priori knowledge. But she then acknowledges that:

Steiner transgressed the limits to knowledge set by Kant, claiming that we can discover, through the disciplined development of our philosophical thinking, something equivalent to the laws of mathematics that point beyond the boundary between sensible and supersensible knowledge.

When a [human] reaches the stage of being able to think of other properties of the world independently of sense-perception in the same way as [s]he is able to think mathematically of geometrical forms and arithmetical relations of numbers, then [s]he is fairly on the path to spiritual knowledge. (Steiner, 1904, para. 4).

With respect to this point, Gidley further notes:

Steiner (1904) elaborated his point, noting that the development of non-Euclidian geometry, particularly the contributions of Leibniz and Newton to Infinitesimal Calculus, shifted mathematical reasoning to an important new boundary line, whereby we "find ourselves continually at the moment of the genesis of something sense-perceptible from something no longer sense-perceptible" (para. 9). He makes a clear distinction, however, between the quantitative nature of the mathematical laws of the sense-perceptible, and the qualitative nature of the analogous philosophical laws of the supersensible (Steiner, 1904).

Beauty: It could be considered strange that the seemingly incommensurable theology and mathematics should share a long-recognized preoccupation with beauty and aesthetics.

This has been explored from a variety of perspectives (Andreas Christiansen, The Beauty and Spirituality of Mathematics: a review essay, International Journal of Education and the Arts, 2009; Subrahmanyan Chandrasekhar, Truth and Beauty. Aesthetics and Motivations in Science, 1987; Ronald Glasberg, Mathematics and Spiritual Interpretation: a bridge to genuine interdisciplinarity, Zygon, 2003; Elliot Nelson, A Theology of Mathematics: Mathematical Beauty, Until a Seed Dies, May 2008)

Creative insight: Mathematics and theology share as special appreciation of "insight", nourished by imaginative speculation:

in mathematics this takes the form of much valued recognition ("in a flash") of a "pattern that connects".
for theology this insight is typically framed as a "revelation" -- possibly as a grace or gift from a transcendental, supernatural reality.

The emergence of insight is intimately related to the mysterious processes of creativity, especially in mathematics. These processes are most evident and comprehensible through humour. These processes have been the focus of a valuable review (Matthew M. Hurley,, et. al., Inside Jokes: using humor to reverse engineer the mind, 2011). This is concerned with "the epistemic predicament of agents in the world and a class of models of cognition that can successfully deal with that predicament". From such a perspective, a case has been separately made for the role of humourin relation to the argument above (Humour and Play-Fullness Essential integrative processes in governance, religion and transdisciplinarity, 2005).